Charlie Gard's parents have renewed a legal fight to take their terminally ill baby son to the United States for treatment.
Chris Gard and Connie Yates, who are in their 30s and come from Bedfont, west London, want 11-month-old Charlie, who suffers from a rare genetic condition and has brain damage, to undergo a therapy trial in America.
A judge has begun overseeing the latest round of litigation at a High Court hearing in London.
Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, have said therapy proposed by a doctor in America is experimental and would not help.
They say life-support treatment should stop.
Charlie's parents had asked European court judges in Strasbourg, France, to consider their claims after losing battles in the High Court, Court of Appeal and Supreme Court in London.
But Strasbourg judges have refused to intervene.
The couple want a High Court judge to take a fresh look at the case.
Mr Justice Francis is overseeing a preliminary hearing in the Family Division of the High Court.
Lawyers representing the couple said they wanted to be allowed to "remove" Charlie from Great Ormond Street for treatment.
They said seven international experts had supported the treatment the couple wanted Charlie to have.
Lawyers said there was "encouraging" evidence.
Mr Justice Francis said he would have to be persuaded that something had happened which would change a judge's mind.
He said a judge could make a different decision if there was "new and powerful" evidence.
The judge said: "There is not a person alive who would not want to save Charlie."
Mr Justice Francis said: "If there is new evidence I will hear it."
But the judge said Charlie had structural brain damage.
He said the evidence had been that the structural brain damage could not be reversed.
Lawyers representing Charlie's parents said evidence indicated a "small chance" of brain recovery.
They said Charlie's case involved "cutting edge genetic science".
Lawyers said there was a "good prospect" of further evidence producing a different result.
Mr Justice Francis had ruled in April that ending life-support treatment would be in Charlie's best interests after a High Court trial.
Lawyers representing Charlie's parents suggested that another judge should analyse any fresh evidence.
Mr Justice Francis disagreed. "I did my job," he said. "I will continue to do my job."
Mr Justice Francis added: "If you bring new evidence to me and I consider that evidence changes the situation ... I will be the first to welcome that outcome."
Lawyers for Charlie's parents said there was "a chance for Charlie" and it was a chance that was "worth taking".
Mr Justice Francis said Charlie's parents would have to set out new information which might justify a different decision.
Lawyers for Great Ormond Street, and a guardian independently representing Charlie, said they were struggling to identify new evidence or new research.